If the sum of the first n terms of a series is n(2n+1), then what is the nth term?

This question was previously asked in
NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. 4n - 1
  2. 4n
  3. 4n + 1
  4. 4n + 3

Answer (Detailed Solution Below)

Option 1 : 4n - 1
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Detailed Solution

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Explanation:

Given

Sn = n(2n + 1), Sn–1 = (n – 1)(2n – 1) 

nth term = Sn – Sn – 1

= n(2n + 1) – (n – 1)(2n–1)

=  4n – 1

∴ Option (a) is correct.

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